21 ideas
13030 | Extensionality: ∀x ∀y (∀z (z ∈ x ↔ z ∈ y) → x = y) [Kunen] |
13032 | Pairing: ∀x ∀y ∃z (x ∈ z ∧ y ∈ z) [Kunen] |
13033 | Union: ∀F ∃A ∀Y ∀x (x ∈ Y ∧ Y ∈ F → x ∈ A) [Kunen] |
13037 | Infinity: ∃x (0 ∈ x ∧ ∀y ∈ x (S(y) ∈ x) [Kunen] |
13038 | Power Set: ∀x ∃y ∀z(z ⊂ x → z ∈ y) [Kunen] |
13034 | Replacement: ∀x∈A ∃!y φ(x,y) → ∃Y ∀X∈A ∃y∈Y φ(x,y) [Kunen] |
13039 | Foundation:∀x(∃y(y∈x) → ∃y(y∈x ∧ ¬∃z(z∈x ∧ z∈y))) [Kunen] |
13036 | Choice: ∀A ∃R (R well-orders A) [Kunen] |
13029 | Set Existence: ∃x (x = x) [Kunen] |
13031 | Comprehension: ∃y ∀x (x ∈ y ↔ x ∈ z ∧ φ) [Kunen] |
13040 | Constructibility: V = L (all sets are constructible) [Kunen] |
9358 | There are several logics, none of which will ever derive falsehoods from truth [Lewis,CI] |
9357 | Excluded middle is just our preference for a simplified dichotomy in experience [Lewis,CI] |
9364 | Names represent a uniformity in experience, or they name nothing [Lewis,CI] |
9362 | Necessary truths are those we will maintain no matter what [Lewis,CI] |
9365 | We can maintain a priori principles come what may, but we can also change them [Lewis,CI] |
9361 | We have to separate the mathematical from physical phenomena by abstraction [Lewis,CI] |
21093 | Friendship without community spirit misses out on the main part of virtue [Hume] |
21091 | It would be absurd if even a free constitution did not impose restraints, for the public good [Hume] |
21092 | Nobility either share in the power of the whole, or they compose the power of the whole [Hume] |
9363 | Science seeks classification which will discover laws, essences, and predictions [Lewis,CI] |